The cyclone has pulling a circuit in the ocean to the country's northwest for a day, and is now not expected to reach the second-biggest island, Vanua Levu, until late tomorrow.
Mona has winds as high as 100 km/hr at its centre, although the authorities are concerned about the volume of rain it will bring.
This afternoon, it was about 380km north-northwest of Yasa-i-Rara, or about 460km northwest of Labasa, the main town on Vanua Levu.
Despite its weakening, warnings remain in force for much of Fiji, and authorities spent Saturday clearing drains, boarding-up houses and businesses, and opening evacuation centres.
It is still forecast to move across the country on Sunday and Monday, passing directly over Vanua Levu, and then skirting close to the east of the main island, Viti Levu, including the capital Suva.
Photo Facebook Ronald Kumar. Caption: Water levels rise in Navua River, Fiji